M190 Exam 2 Question 2: A steady wind blows a red kite towards the west. The height of the red kite follows the path along f (x) = 50 - 2 (x - 10)2 from a horizontal position of x - 0 feet to x - 75 feet. Complete the following. A) Sketch a diagram representing the path of the red kite. (2 points) B) Set up a simplified integral (in terms of x) for the path that the red kite travels. (6 points) C) Set up a trigonometric substitution and rewrite the simplified integral from B) (in terms of 0). Be sure to include and label a triangle with the substitution functions for full credit. (4 points) D) Given the following formulas, simplify the integral from C) and calculate the distance traveled by the red kite to EIGHT decimal places. (3 points) Helpful Integration Formulas: S cos3 0 de - sin 0 - _ sin3 0 + C S sin' 0 de = - cos 0 + =cos3 0 + C S tan' 0 d0 = > sec2 0 - In | sec 0| + C f sec3 0 d0 - - sec 0 tan 0 + ; In | sec 0 + tane + C